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Vandaag is het 16 July 2018

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Painting stairs - math puzzle

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To enter the house of the professor, you first have to walk up a stairs which consists out of twenty steps. The professor thinks his stairs are boring so he decides to paint them. He buys two colors, yellow and green.

Every step will be either painted yellow or green and moreover the professor does not want to have two yellow steps directly after each other. In how many ways can the professor paint his stairs? And what is the name of the professor?
stairs

Answer

The professor can paint his stairs in 17711 ways and most probably he is called Fibonaci.